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The Correct Answer and Explanation is:
To determine how many loan officers are needed to process 100 loan applications per day, given the following:
Given Information:
- Each application takes 20 minutes
- Each officer works 7 hours per day
- Utilization rate is 80%
- We are to round the final answer to the nearest whole number
Step 1: Calculate how many applications one officer can process per day
- First, convert 7 hours to minutes: 7 hours×60=420 minutes7 \text{ hours} \times 60 = 420 \text{ minutes}
- Since the officer is only working at 80% utilization, we multiply: 420×0.80=336 effective working minutes per day420 \times 0.80 = 336 \text{ effective working minutes per day}
- Each application takes 20 minutes, so: 33620=16.8 applications per officer per day\frac{336}{20} = 16.8 \text{ applications per officer per day}
Step 2: Calculate how many officers are needed to process 100 applications
Now divide total applications needed by the number of applications one officer can handle: 10016.8≈5.95\frac{100}{16.8} \approx 5.95
Since we can’t hire a fraction of a person, round up to the nearest whole number: 6 loan officers\boxed{6 \text{ loan officers}}
✅ Final Answer: 6 Loan Officers
🔍 300-Word Explanation:
To determine appropriate staffing levels, it’s essential to account for both the actual working hours and the efficiency of the workforce. In this scenario, the bank expects to process up to 100 loan applications daily. The key pieces of information are the time it takes to process one application (20 minutes), the number of hours each loan officer works (7 hours), and the utilization rate (80%).
First, convert 7 working hours into minutes (since processing time is in minutes). Seven hours is equal to 420 minutes. However, due to breaks, meetings, or administrative tasks, loan officers are only working productively for 80% of that time. Hence, 80% of 420 minutes is 336 minutes of actual productive time.
Next, we calculate how many applications one officer can process in those 336 minutes. Since each application takes 20 minutes, each officer can handle 336 ÷ 20 = 16.8 applications per day.
To meet the bank’s goal of processing 100 applications daily, we divide the total applications needed (100) by the number each officer can handle (16.8). This yields about 5.95. Since partial staff cannot be hired and full coverage is necessary, we round up to the nearest whole number.
Thus, the bank would need to employ 6 loan officers to ensure that 100 loan applications can be processed each day, accounting for processing time, work hours, and utilization.